Energy-limited Massive Random Access via Noisy Group Testing

We consider a random access scheme with a massive number of low-energy wireless devices, where a small but arbitrary subset of them can be active at a given time. We develop a solution to this problem via the noisy group testing framework, where the goal is to identify with high probability a small set of defectives in a large set of items with minimum number of noisy binary tests. We translate the power constraint for the wireless devices to a constraint on the number of tests each item can participate in the group testing problem. We present fundamental upper and lower bounds on the length of the codewords in terms of the total number of devices, the number of active devices, the error probability, the noise and the power constraint. We conclude with a scheme that enjoys low decoding complexity under this model.